Subspace Learning. Our work follows the methodology of
subspace learning. Although subspace learning has a long history, Kuo
et al. [1]} built a link between subspace
learning and the convolutional operations in CNNs recently. A set of
convolutional filters in a given convolutional layer of a CNN can be
interpreted as a set of filters in one filter bank. The filter
parameters in CNNs are obtained via end-to-end optimization through
back-propagation. However, in subspace learning, filter parameters are derived by the
statistical analysis of pixel correlations inside a local region covered
by the filter. For example, for a filter of size 5x5x3, where 5x5 corresponds to the spatial window size and 3 corresponds to the three color channels, we would examine
the correlations between the 5*5*3 = 75 pixels. A variant of principal
component analysis (PCA), called the Saab (Subspace approximation via
adjusted bias) transform, was introduced in [1]}
and used to determine filter parameters. The concept of multiple
convolutional layers can be ported to subspace learning, leading to
successive subspace learning (SSL), and the corresponding architecture
is called the PixelHop [3]}. PixelHop offers an
unsupervised and feedforward feature learning process. Neither
back-propagation nor labels are needed in deriving filter parameters. SSL
has been applied to image classification [3]} and 3D
point cloud classification [5]}, among many others.
In image forensics, DefakeHop [6]} was proposed to
detect deepfake videos.
